Miscellaneous incidences of convergence theories in optimization and nonlinear analysis I: Behavior of solutions

We examine some connections between convergence theories and optimization. In particular we study the Lipschitzian character of the infimal value function with respect to variations of the objective function. We also study the approximate solution multifunction for convex and nonconvex objective functions.

[1]  Jean-Paul Penot,et al.  On the convergence of subdifferentials of convex functions , 1993 .

[2]  S. Yamamuro,et al.  Differential Calculus in Topological Linear Spaces , 1974 .

[3]  U. Mosco.  Convergence of convex sets and of solutions of variational inequalities , 1969 .

[4]  J. Penot,et al.  The Joly topology and the Mosco-Beer topology revisited , 1993, Bulletin of the Australian Mathematical Society.

[5]  Jean-Paul Penot,et al.  Preservation of persistence and stability under intersections and operations, part 1: Persistence , 1993 .

[6]  Abdellatif Moudafi,et al.  Quantitative stability analysis for maximal monotone operators and semi-groups of contractions , 1993 .

[7]  Gerald Beer,et al.  On Mosco convergence of convex sets , 1988, Bulletin of the Australian Mathematical Society.

[8]  J. Moreau,et al.  Intersection of moving convex sets in a normed space. , 1975 .

[9]  Tosio Kato.  Perturbation theory for linear operators , 1966 .

[10]  D. Azé,et al.  Intrinsic Bounds for Kuhn-Tucker Points of Perturbed Convex Programs , 1995 .

[11]  R. Rockafellar.  Conjugate Duality and Optimization , 1987 .

[12]  S. Dolecki.  Convergence of minima in convergence spaces 1 , 1986 .

[13]  Roberto Lucchetti,et al.  The topology of theρ-hausdorff distance , 1991 .

[14]  J. Penot.  On regularity conditions in mathematical programming , 1982 .

[15]  J. Aubin,et al.  APPLIED FUNCTIONAL ANALYSIS , 1981, The Mathematical Gazette.

[16]  Jean-Paul Penot,et al.  The cosmic Hausdorff topology, the bounded Hausdorff topology and continuity of polarity , 1991 .

[17]  R. Wets,et al.  Quantitative stability of variational systems. I. The epigraphical distance , 1991 .

[18]  U. Mosco.  On the continuity of the Young-Fenchel transform , 1971 .

[19]  Gerald Beer,et al.  On some inverse stability problems for the epigraphical sum , 1991 .

[20]  Jean-Paul Penot,et al.  Operations on convergent families of sets and functions , 1990 .

[21]  Jean-Paul Penot,et al.  Topologies and convergences on the space of convex functions , 1992 .

[22]  R. T. Rockafellar,et al.  Gradients of convex functions , 1969 .

[23]  G. Beer.  On the Young-Fenchel transform for convex functions , 1988 .

[24]  Roger J.-B. Wets,et al.  Continuity of some convex-cone-valued mappings , 1967 .

[25]  Gerald Beer,et al.  Conjugate convex functions and the epi-distance topology , 1990 .

[26]  H. Fédérer.  Geometric Measure Theory , 1969 .

[27]  C. Castaing,et al.  Convex analysis and measurable multifunctions , 1977 .

[28]  Roger J.-B. Wets,et al.  ISOMETRIES FOR THE LEGENDRE-FENCHEL TRANSFORM , 1986 .

[29]  Roger J.-B. Wets,et al.  Quantitative Stability of Variational Systems II. A Framework for Nonlinear Conditioning , 1993, SIAM J. Optim..

[30]  H. Attouch.  Variational convergence for functions and operators , 1984 .